Chapter 10. Orthogonal Polynomials

  1. André I. Khuri

Published Online: 26 MAR 2003

DOI: 10.1002/0471394882.ch10

Advanced Calculus with Applications in Statistics, Second Edition

Advanced Calculus with Applications in Statistics, Second Edition

How to Cite

Khuri, A. I. (2002) Orthogonal Polynomials, in Advanced Calculus with Applications in Statistics, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471394882.ch10

Author Information

  1. University of Florida, Gainesville, Florida, USA

Publication History

  1. Published Online: 26 MAR 2003
  2. Published Print: 1 NOV 2002

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. David J. Balding,
  2. Peter Bloomfield,
  3. Noel A. C. Cressie,
  4. Nicholas I. Fisher,
  5. Iain M. Johnstone,
  6. J. B. Kadane,
  7. Louise M. Ryan,
  8. David W. Scott,
  9. Adrian F. M. Smith and
  10. Jozef L. Teugels

ISBN Information

Print ISBN: 9780471391043

Online ISBN: 9780471394884

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Keywords:

  • Chebyshev polynomial;
  • Cornish–Fisher expansion;
  • Gram–Charlier series;
  • Hermite polynomial;
  • hypergeometric probability;
  • Jacobi polynomial;
  • Laguerre polynomial;
  • least-squares approximation;
  • Legendre polynomial;
  • Rodrigues formula

Summary

This chapter provides an exposition of the properties of orthogonal polynomials, including Legendre, Jacobi, Chebyshev, Hermite, and Laguerre polynomials. The last section includes some applications in statistics, such as approximation of density functions and quantiles of distributions, approximation of the normal integral, estimation of unknown densities, and the calculation of hypergeometric probabilities.